Sitecore uses aspnet membership provider and stores the user profile information in the aspnet_Profile table. All the properties are serialized into the PropertyNames / PropertyValuesString columns.
https://msdn.microsoft.com/en-au/library/aa478953.aspx
Run below query onto Sitecore Core database on aspnet_profile table.
SELECT TOP 1000 [UserId]
,[PropertyNames]
,[PropertyValuesString]
,[PropertyValuesBinary]
,[LastUpdatedDate]
FROM [Website826_Core].[dbo].[aspnet_Profile]
You will be able to set the new properties from web.config file using below tags. Have a look at your application's web config and check profile tag for exact details.
<profile defaultProvider="sql" enabled="true" inherits="Sitecore.Security.UserProfile, Sitecore.Kernel">
<providers>
<clear />
<add name="sql" type="System.Web.Profile.SqlProfileProvider" connectionStringName="core" applicationName="sitecore" />
<add name="switcher" type="Sitecore.Security.SwitchingProfileProvider, Sitecore.Kernel" applicationName="sitecore" mappings="switchingProviders/profile" />
</providers>
<properties>
<clear />
<add type="System.String" name="SC_UserData" />
</properties>
</profile>